For several years, multicarrier modulations have aroused large interest. This is in particular justified in the case of mobile phone communications, where their effectiveness has already been demonstrated for broadcasting radio signals, with, first of all, the Digital Audio Broadcasting system (DAB) [1] (for the sake of simplification and legibility, all references mentioned in the present description have been grouped in Appendix E) but also in high rate transmissions over telephone two-wire lines with ADSL (Asymmetric Digital Subscriber Line) and VDSL (Very high bit rate Digital Subscriber Line) systems [2]
In the usual multicarrier modulation schemes, a set of carrier frequencies selected in order to meet time and frequency orthogonality conditions, is multiplexed. This is the so-called Orthogonally Frequency Division Multiplex (OFDM).
A modulation without any offset (Synchronous Modulation) (SM) or with an offset (Offset Modulation) (OM) may be associated with each of the carriers. This now results in the OFDM/SM and OFDM/OM systems, respectively. In particular, by associating a quadrature amplitude modulation, with or without any offset, with each of the carriers, OFDM/QAM (Quadrature Amplitude Modulation) and OFDM/OQAM (Offset QAM) modulations are produced respectively. This latter modulation operates without any guard interval and also provides a wider possibility of choice as regards the prototype function [3], [4].
However, optimality of OFDM is only ensured by its orthogonality, in the case of transmission channels which may be assimilated with additive white and gaussian noise. In all other cases, OFDM's optimality is not guaranteed.
From this point of view, biorthogonal multicarrier modulations (BFDM) provide further possibilities and in particular they may be a better compromise with regards to mobile radio phone type channels which are dispersive in both time and frequency [5].
Furthermore, with an offset biorthogonal modulation (BFDM/OM), the advantage of OFDM/OM may be retained with the possibility of obtaining prototype functions well localized in time and in frequency.
As an indication, a short reminder of the essential definitions relating to the mathematical aspects related to modulations of the BFDM/OM type is given in Appendix A. These aspects have already been the object of publications, with the designation BFDM/OFDM, also retained in the appendices of the present description.
A discretization technique for BFDM/OM modulation systems has already been suggested in a recently submitted article [6]. However, the approach described in [6], [7] is essentially based on discretization of continuous equations which extend the formalism introduced in the continuous domain to the discrete domain, in reference [4] for OFDM/OM.
For OFDM/OM, the use of a mathematical transform and of the reverse transform (conventionally FFT−1 then FFT) is therefore assumed. The discretized signal is then truncated.
The object of the invention is notably to provide a new technique for modulating and demodulating a BFDM/OM signal which is more effective and easier to implement as known techniques.
Thus, an object of the invention is to provide such modulation and demodulation techniques which are able to ensure theoretically, that symbol interference (IES) and channel interference (IEC) are exactly zero, on a finite support.
An object of the invention is also to provide such techniques with which devices may be made which structurally fulfil the cancellation of IES and IEC.
Another object of the invention is to provide such techniques, which provide the implementation of prototype functions, either symmetrical or not and either identical or not, both upon transmission and reception.
Still another object of the invention is to provide such modulation and demodulation techniques with which reconstruction delays may be reduced and controlled, for example for real time or interactive applications. In other words, one object is to provide such techniques with which, for prototype filters of a given length, reconstruction delays may be obtained which are not set (and which may therefore be smaller than those of OFDM/OM).
An object of the invention is also to provide such techniques which are optimum, with respect to distortions, produced by a gaussian channel and/or by non-gaussian channels which are not simply reduced to additive white gaussian noise.
Still another object of the invention, is to provide such techniques, with which higher performances, as compared with known techniques, may be obtained, in terms of localization of the transform.
An object of the invention is also to provide modulation and/or demodulation and more generally devices for transmitting and/or receiving signals, which are easy and not very expensive to make and implement.